TOKYO, Sept 28 (Reuters) - Japanese stocks rallied to near 27-year highs and posted the biggest monthly gain since last October, helped by the prospect of a weaker yen and a strong U.S. economy boosting exporters profits. During intraday trade, the Nikkei share average hit as high as 24,286.10, the highest level since November 1991.

But the benchmark index came off slightly to close just 1.4 percent higher at 24,120.04, a shade below the Jan. 23 closing high of 24,124.15.

The index advanced 1 percent for the week, making a third straight week of gains.

For the month, it surged 5.5 percent to post the biggest monthly gain since last October, on the earning hopes and partly as rising U.S. yields helped lift shares of financial firms, which hunt for high-yielding products such as foreign bonds.

"Still, the majority of buyers are seen short-term foreign investors, but mid-to-long term investors will probably have to catch up with the rally as well," said Shogo Maekawa, global market strategist at JPMorgan Asset Management.

The dollar-yen level - which traded above 113.67 to hit a fresh nine-month high on Friday - is raising hopes for a brighter earnings for Japanese companies as a weaker yen boosts manufacturers' profits made abroad when repatriated.

"There are many companies which have based their foreign currency expectations at 105 yen this year so there are hopes that companies may revise up their forecasts," said Shusuke Yamada, chief Japan FX and equity strategist at Bank Of America Merrill Lynch.

Analysts said that foreign investors, who have been net sellers this year, are buying back Japanese stocks to catch up with the gains in the U.S. market, where both the S&P 500 index and the Dow Jones Industrial Average have hit all-time highs this month.

One loser was Panasonic Corp, which provides batteries for Tesla Inc. It dropped for a third day and was 1 percent lower after the top U.S. securities regulator on Thursday accused Tesla Chief Executive Elon Musk of fraud.

The Securities and Exchange Commission (SEC) sought to remove him from his role in charge of the electric car company, saying he made a series of "false and misleading" tweets about potentially taking Tesla private last month.